US Patent 7539929 Error correction for data communication

Generating a check matrix includes defining a generator function operable to yield check bits associated with a word. A set of primitive elements is calculated from the generator function. A set of check matrix columns is generated, where each check matrix column includes a matrix having a subset of the set of primitive elements. A check matrix is generated from a subset of the set of check matrix columns, where the check matrix yields a syndrome that comprises an error pattern for the word. The check matrix is reported.